If you prefer, kale may be substituted. Cheddar cheese is just a suggestion; feel free to substitute what you find at the market or happen to have in the refrigerator. It should be assertive; mild cheeses won’t stand up to the garlicky greens.

Steps

1. Bring large saucepan filled with water to boil. Season generously with salt and add chard leaves. Simmer until just tender, about 2 minutes. Drain and cool under running water. Squeeze dry, chop coarsely and set aside.
2. Combine 2 tablespoons of oil, garlic, and crushed pepper flakes in large, nonstick or well-seasoned skillet over medium-high heat. Cook, stirring frequently, until garlic just begins to color, about 2 minutes. Add greens and cook until glossy and covered in oil and garlic, about 2 minutes. Drizzle with lemon juice to taste; transfer to bowl and set aside.
3. Return pan to burner and reduce heat to medium. Add 1 tablespoon of oil to pan along with chard stems, onion, sugar, and large pinch salt. Cook, stirring frequently, until onions have softened and are beginning to brown, 7 to 10 minutes. Push onion and chard mixture to ring around outside of pan; add remaining 1 tablespoon of oil to center of pan and crack eggs evenly around center of pan. Season eggs with salt and pepper and cover pan. Cook until eggs are just set but yolks are still runny, 2 to 4 minutes. Top with cheese, recover, and cook until cheese has just melted, about 2 minutes longer. Divide greens evenly amongst rolls, top each roll with an egg, and spread onion mixture over top. Serve immediately.